TUN: Detecting Significant Points in Persistence Diagrams with Deep Learning
This addresses the challenge of reliable interpretation of persistence diagrams for applications requiring automated decision-making, representing an incremental improvement.
The paper tackled the problem of automatically identifying significant points in persistence diagrams for topological data analysis, proposing TUN, a deep learning network that outperforms classic methods in experiments.
Persistence diagrams (PDs) provide a powerful tool for understanding the topology of the underlying shape of a point cloud. However, identifying which points in PDs encode genuine signals remains challenging. This challenge directly hinders the practical adoption of topological data analysis in many applications, where automated and reliable interpretation of persistence diagrams is essential for downstream decision-making. In this paper, we study automatic significance detection for one-dimensional persistence diagrams. Specifically, we propose Topology Understanding Net (TUN), a multi-modal network that combines enhanced PD descriptors with self-attention, a PointNet-style point cloud encoder, learned fusion, and per-point classification, alongside stable preprocessing and imbalance-aware training. It provides an automated and effective solution for identifying significant points in PDs, which are critical for downstream applications. Experiments show that TUN outperforms classic methods in detecting significant points in PDs, illustrating its effectiveness in real-world applications.